Questionc) $\frac{(10 x)^{-1} y^{3}}{15 x^{3} y^{-3}}$

Studdy Solution

STEP 1

What is this asking? Simplify this fraction with variables $x$ and $y$ . Watch out! Don't forget the rules of exponents!
A negative exponent means "reciprocal," not "negative number."

STEP 2

1. Rewrite the expression
2. Simplify the expression

STEP 3

Remember, a negative exponent means "one over." So, $(10x)^{-1}$ becomes $\frac{1}{10x}$ .
Let's rewrite our expression: $\frac{\frac{1}{10x} \cdot y^3}{15x^3 y^{-3}}$

STEP 4

$y^{-3}$ becomes $\frac{1}{y^3}$ .
Let's rewrite our expression again: $\frac{\frac{1}{10x} \cdot y^3}{15x^3 \cdot \frac{1}{y^3}}$

STEP 5

We can simplify the fraction by multiplying the numerator and denominator by $y^3$ .
This is like multiplying by one, so it doesn't change the value of the expression: $\frac{\frac{1}{10x} \cdot y^3 \cdot y^3}{15x^3 \cdot \frac{1}{y^3} \cdot y^3}$

STEP 6

In the numerator, $y^3 \cdot y^3$ becomes $y^6$ .
In the denominator, $\frac{1}{y^3} \cdot y^3$ becomes $1$ .
So, we have: $\frac{\frac{1}{10x} \cdot y^6}{15x^3}$

STEP 7

We can rewrite this as: $\frac{y^6}{10x \cdot 15x^3}$

STEP 8

In the denominator, we have $x \cdot x^3 = x^4$ .
Remember, when multiplying variables with exponents, we add the exponents.
Don't forget that $x$ is the same as $x^1$ .
So, our expression becomes: $\frac{y^6}{10 \cdot 15 \cdot x^4}$

STEP 9

$10 \cdot 15 = 150$ , so we have: $\frac{y^6}{150x^4}$

STEP 10

Our simplified expression is $\frac{y^6}{150x^4}$ !

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